In the related art, a NOx-occlusion-reduction-type catalyst is known, as a catalyst for reducing and purifying a nitrogen compound (NOx) in exhaust emitted from an internal combustion engine. When the exhaust is in a lean atmosphere, the NOx-occlusion-reduction-type catalyst occludes NOx contained in the exhaust, and when the exhaust is in a rich atmosphere, the NOx-occlusion-reduction-type catalyst detoxifies and releases the occluded NOx with hydrocarbon contained in the exhaust by reduction and purification. For this reason, when a NOx occlusion amount of the catalyst reaches a predetermined amount, it is necessary to periodically perform NOx purge of enriching the exhaust by exhaust pipe injection or post injection so as to recover a NOx occlusion capacity (for example, refer to Patent Documents 1 and 2).